Problem: Evaluate the infinite geometric series: $$\frac{3}{2}-\frac{2}{3}+\frac{8}{27}-\frac{32}{243}+\dots$$
Answer: The series has first term $\frac{3}{2}$ and common ratio $\frac{-4}{9}$, so the formula yields: $\cfrac{\frac{3}{2}}{1-\left(\frac{-4}{9}\right)}=\boxed{\frac{27}{26}}$.